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The α-dimensional measure of the graph and set of zeros of a Brownian path

Published online by Cambridge University Press:  24 October 2008

S. J. Taylor
S. J. Taylor
Affiliation:
PeterhouseCambridge
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Extract

In a recent joint paper (1) with Prof. Besicovitch we announced the conjecture that for almost all one-dimensional Brownian paths, the set of zeros has dimensional number ½, and zero A½-measure. It is the purpose of this paper to give a proof of this result. In doing so we consider the graph C(ω) of a Brownian path ω as a point set in the plane, and prove that, with probability 1, C(ω) has dimensional number ¾ and zero Λ¾-measure.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 2 , April 1955 , pp. 265 - 274
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

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